Sketch
August 1, 2019
10:51 AM
Title: The Mysteries of BF.
Abstract: The BF quantum field theory on one hand, and prior art regarding finite type invariants of w-knots on the other hand, suggest that there should be a "Kontsevich Integral" for general 2-knots in 4-space (of not necessarily the "simple" or "welded" or "w" type). Where is it? Why don't we know about it? Why aren't we studying it?
Contents.
Apologize for being out of shape in matters 4D.
A quick summary of CS:
a. The CS Lagrangian. Using Faddeev-Popov/BRST/Feynman Diagrams leads to CSI.
b. CSI in a quick picture.
c. Converges! Invariant! (Hard).
d. Evaluatable in a quick picture. (Porrier's)
e. Characterizable in a quick picture. (Bracelets).
A quick summery of BF:
a. The BF Lagrangian. Using BV/Feynman Diagrams leads to CSI.
b. CSI in a quick picture.
c. Converges? Invariant? (Cattaneo-Rossi, etc).
d. Evaluatable??
e. Characterizable?
A quick summary of the w-story.
Alternative:
Abstract: This will be a "large structures" talk. I will explain how several large structures fit together nicely in 3D: universal finite type invariants, quantum field theory, configuration space integrals, and perhaps a bit more. The picture isn't so clean in 4D, but it isn't yet clear if this is simply because we didn't work hard enough yet, or if things are intrinsically different.
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